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Research Papers: Design of Mechanisms and Robotic Systems

Kinematic Model of Planetary Roller Screw Mechanism With Run-Out and Position Errors

[+] Author and Article Information
Xiaojun Fu, Shangjun Ma, Ruiting Tong

Shaanxi Engineering Laboratory for
Transmissions and Controls,
Northwestern Polytechnical University,
Xi'an 710072, China

Geng Liu

Shaanxi Engineering Laboratory for
Transmissions and Controls,
Northwestern Polytechnical University,
Xi'an 710072, China
e-mail: npuliug@nwpu.edu.cn

Teik C. Lim

Provost & Vice President for Academic Affairs,
University of Texas at Arlington,
Arlington, TX 76019

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received December 17, 2016; final manuscript received December 1, 2017; published online January 25, 2018. Assoc. Editor: David Myszka.

J. Mech. Des 140(3), 032301 (Jan 25, 2018) (10 pages) Paper No: MD-16-1841; doi: 10.1115/1.4039005 History: Received December 17, 2016; Revised December 01, 2017

A kinematic model of the planetary roller screw mechanism (PRSM) is proposed, which accounts for the run-out errors of the screw, roller, nut, ring gear, and carrier, and the position errors of the nut and the pinhole in the carrier. The roller floating region, which contains all the possible positions of the roller inside the pinhole, is obtained by analyzing the axial clearances between mating thread surfaces and the radial clearance between the roller and carrier. The proposed model is based on the constraint that the set of roller floating region is not empty. Then, the additional rigid-body movement on the nut is derived and the path of motion transfer from the screw to the nut is obtained. According to the fundamental property of rigid-body kinematics, the axial velocity of the nut is derived and the transmission error of the PRSM is calculated. The proposed model is verified by comparing the calculated transmission error with experimental one. The results show that the transmission error of the PRSM with run-out and position errors is cyclic with a period corresponding to the rotation period of the screw and the magnitude of the transmission error can be much larger than the lead error of the screw. Besides, due to the run-out and position errors, the roller can move radially or transversally inside the pinhole of the carrier when the elements in the PRSM are regarded as rigid bodies.

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Figures

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Fig. 1

Run-out errors of the (a) screw and (b) roller #q

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Fig. 2

Run-out errors of the nut, ring gear, and carrier

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Fig. 3

Position error of the nut

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Fig. 4

Position error of the pinhole #q in the carrier

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Fig. 5

Positions of the screw, nut, roller #q in the global coordinate system O-XYZ

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Fig. 6

Radial clearance between the roller #q and carrier

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Fig. 7

Floating region of the roller #q

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Fig. 8

Additional rigid-body movement on the nut

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Fig. 9

Kinematics analysis of the spur–ring gear pair at the nut-roller #q interface

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Fig. 10

Kinematics analysis at the screw-roller #q* and nut-roller #q* interfaces

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Fig. 11

Structure of the transmission error test bench of the PRSM

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Fig. 12

Maximum and minimum εqrx of in the set Λq versus time: (a) roller #1, (b) roller #2, and (c) roller #3

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Fig. 13

Transmission error ΔN of the PRSM

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